The value of x from the given diagram is 17
<h2>Vertically opposite angles</h2>
From the given diagram, m<2 and m<3 are vertically opposite since they form angles from the intersection of lines at the point X
Given that;
- m<2 = 4x + 2
- m<3 = 5x - 15
Equate both expressions to have:
m<2 = m<3
4x + 2 = 5x - 15
4x - 5x = -15 - 2
-x = -17
x = 17
Hence the value of x from the given diagram is 17.
Learn more on vertical angles here; brainly.com/question/1673457
Answer:
29/28
Step-by-step explanation:
"Completing the square" is the process used to derive the quadratic formula for the general quadratic ax^2+bx+c=0. Suppose you did not know the value of a,b, or c of the quadratic...
ax^2+bx+c=0 You need a leading coefficient of one for the process to work, so you divide the whole equation by a
x^2+bx/a+c/a=0 now you move the constant to the other side of the equation
x^2+bx/a=-c/a now you halve the linear coefficient, square that, then add that value to both sides, ie, (b/(2a))^2=b^2/(4a^2)...
x^2+bx/a+b^2/(4a^2)=b^2/(4a^2)-c/a now the left side is a perfect square...
(x+b/(2a))^2=(b^2-4ac)/(4a^2) now take the square root of both sides
x+b/(2a)=±√(b^2-4ac)/(2a) now subtract b/(2a) from both sides
x=(-b±√(b^2-4ac))/(2a)
It is actually much simpler keeping track of everything when using known values for a,b, and c, but the above explains the actual process used to create the quadratic formula, which the above solution is. :)
Ryan: y=10x+25 Alex: y=11x+20
a) Mr. Smith should choose Alex because the price would be $42 compared to Ryan which would be $45
b) Mr.Smith could choose either Ryan or Alex because they would both charge $75
<h3>
Answer: 10 metal bats</h3>
"Ratio of wooden bats to metal bats is 2 to 1" basically means "there are twice as many wooden bats (compared to metal ones)". So if we had 3 metal bats, then we'd have 2*3 = 6 wooden bats. If we had 7 metal bats, then we have 14 wooden ones (because 2*7 = 14). And so on. The basic rule is to multiply the amount of metal bats by 2 to get the amount of wooden ones.
We can go in reverse to divide the amount of wooden bats to get the amount of metal ones. So 20/2 = 10 is the amount of metal bats.
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A more formal approach is to use the proportion below to solve for x
20/x = 2/1
20*1 = x*2
20 = 2x
2x = 20
2x/2 = 20/2
x = 10
and we get the same answer.
